Project Euler - Problem 7

Welcome to week 7 of Project Euler.

Problem 7:

Find the 10001st prime.

Details:

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.

What is the 10001st prime number?

Code:

// Find the 10001st prime.

class Problem0007

{

static void Main(string[] args)

{

List primes = new List();

int number = 2;

while (primes.Count() != 10001)

{

bool isPrime = true;

for (var j = 2; j < number; j++)

{

if (number % j == 0)

{

isPrime = false;

break;

}

}

if (isPrime)

{

primes.Add(number);

primes.Sort();

}

number++;

}

primes.Sort();

Console.WriteLine(primes.Last());

Console.ReadLine();

}

}

Solution:

This one is pretty similar to Problem 3 except that instead of making a list of primes of a certain number, we are making a list of primes until the list has a certain number of entries. That, however, is pretty much where the differences end.  I start off my search for primes with the number two (one is not technically a prime number) and go from there. I have a list that is collecting all the primes that are found along the journey.  As soon as a number is found to not be prime, I break out of that iteration of the loop and try again with the next number.  A bool helps me keep track of whether or not it is actually a prime and at the end, if it is, then I add it to my list.  At the end all that needs to be done is sort the list and display the last one.  Done!

Up next week will be problem 8 which is another brute force solution.  The next prime number problem (number 10 I believe), however, is shaping up to be pretty interesting. Until then...

Enjoy!